In the expression $p^2=4q_1$, what does the small $1$ mean?

Question

In the image below there is $p^2 = 4q$ and then a small $1$. What is the name/meaning of this notation? I have never seen it before and can't find what the meaning of it is. Help is appreciated!

See this image:

Answer 1

It is a subscript, indicating that $q_1$ is not necessarily the same as $q$. -- hardmath

The author has established that $p^2$ is divisible by $4$. This makes it possible to write $p^2=4q_1$ where $q_1$ is some integer.

One could use another letter, say, "$p^2=4r$ where $r$ is an integer". But if this process continues, one runs out of letters very soon. Using indices one has an infinite supply of names for objects: $x_1,x_2,x_3,\dots$, and can refer to them in a structured way, e.g., $x_{n+1} = 3x_n$, etc.